Question 701599


<h4>x-intercept</h4>

To find the x-intercept, plug in {{{y=0}}} and solve for x



{{{4x-8y=32}}} Start with the given equation.



{{{4x-8(0)=32}}} Plug in {{{y=0}}}.



{{{4x-0=32}}} Multiply {{{-8}}} and 0 to get 0.



{{{4x=32}}} Simplify.



{{{x=(32)/(4)}}} Divide both sides by {{{4}}} to isolate {{{x}}}.



{{{x=8}}} Reduce.



So the x-intercept is *[Tex \LARGE \left(8,0\right)].



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<h4>y-intercept</h4>

To find the y-intercept, plug in {{{x=0}}} and solve for y



{{{4x-8y=32}}} Start with the given equation.



{{{4(0)-8y=32}}} Plug in {{{x=0}}}.



{{{0-8y=32}}} Multiply {{{4}}} and 0 to get 0.



{{{-8y=32}}} Simplify.



{{{y=(32)/(-8)}}} Divide both sides by {{{-8}}} to isolate {{{y}}}.



{{{y=-4}}} Reduce.



So the y-intercept is *[Tex \LARGE \left(0,-4\right)].



Now let's plot the points *[Tex \LARGE \left(8,0\right)] and *[Tex \LARGE \left(0,-4\right)] which are the x and y intercepts respectively.



{{{drawing(500, 500, -10,10,-10,10,
grid(0),
graph(500, 500, -10,10,-10,10,0)
circle(8,0,0.03),circle(8,0,0.05),circle(8,0,0.08),circle(8,0,0.10),circle(8,0,0.12),
circle(0,-4,0.03),circle(0,-4,0.05),circle(0,-4,0.08),circle(0,-4,0.10),circle(0,-4,0.12)
)}}}



Now draw a straight line through the plotted points to graph {{{4x-8y=32}}}.



{{{ drawing(500, 500, -10,10,-10,10,
grid(0),
graph(500, 500, -10,10,-10,10,(32-4x)/(-8)),
circle(8,0,0.03),circle(8,0,0.05),circle(8,0,0.08),circle(8,0,0.10),circle(8,0,0.12),
circle(0,-4,0.03),circle(0,-4,0.05),circle(0,-4,0.08),circle(0,-4,0.10),circle(0,-4,0.12)
)}}} Graph of {{{4x-8y=32}}}